On some geometric conditions for minimality of DCH-functions via DC-duality approach

Mahide Küçük (), Didem Tozkan () and Yalçın Küçük ()
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Mahide Küçük: Anadolu University
Didem Tozkan: Anadolu University
Yalçın Küçük: Anadolu University

Journal of Global Optimization, 2017, vol. 69, issue 4, No 9, 965 pages

Abstract: Abstract In this study, some optimality conditions for DCH-functions are given in terms of $$\varepsilon $$ ε -faces using DC-duality approach. We introduce some geometric characterizations for the solution set of DCH-minimization problems by means of exposed faces and Minkowski difference. Moreover, we prove that given conditions are independent of the choices of representatives of DCH-functions. Also, some of these conditions are employed to find inf-stationary points for a quasidifferentiable optimization problem (QDP), i.e., the directional derivative of the objective function is a DCH-function. Therefore, we present a condition to find stationary points of a QDP. We give some examples to illustrate obtained results.

Keywords: DC-functions; DCH-functions; Quasidifferential; Minkowski difference; 49J521; 49K99; 90C46 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10898-017-0552-7

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